Branching Fractions and Direct CP Violation in Charmless Three-body Decays of B Mesons

Abstract

Charmless three-body decays of B mesons is studied using a simple model based on the framework of the factorization approach. Hadronic three-body decays receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated three-body decays arise from the $b\to u$ tree transition which can be evaluated using heavy meson chiral perturbation theory valid in the soft meson limit. For penguin-dominated decays, nonresonant signals come mainly from the penguin amplitude governed by the matrix elements of scalar densities $<M_1{M}_2|{\bar{q}}_1{q}_2|0>$. We use the measurements of ${\bar{B}}^0\to K_S{K}_S{K}_S$ to constrain the nonresonant component of $<K\bar{K}|\bar{s}s|0>$. The intermediate vector meson contributions to three-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. While the calculated direct CP violation in $B^{-}\to K^{+}{K}^{-}{K}^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ decays agrees well with experiment in both magnitude and sign, the predicted CP asymmetries in $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ are wrong in signs when confronted with experiment. It has been conjectured recently that a possible resolution to this CP puzzle may rely on final-state rescattering of ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$. Assuming a large strong phase associated with the matrix element $<K\pi |\bar{s}q|0>$ arising from some sort of power corrections, we fit it to the data of $K^{-}{\pi }^{+}{\pi }^{-}$ and find a correct sign for ${\pi }^{-}{K}^{+}{K}^{-}$.

38 pages, Tables III-XI are revised, to appear in Phys. Rev. D

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• Updated Values of Running Quark and Lepton Masses
• Measurement of CP violation in the phase space of $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ and $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$ decays
• Charmless Three-body Decays of B Mesons
• High statistics study of f_0(980) resonance in gamma gamma --> pi^+ pi^- production
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• Interference between f0(980) and rho(770) resonances in B --> pion-pion-kaon decays
• CP asymmetries in three-body B+- decays to charged pions and kaons
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• Resolving B-CP Puzzles in QCD Factorization
• Final state interactions in B+- to K+ K- K+- decays
• Rescattering effects in charmless B_{u,d,s} to P P decays
• Evidence for the decay B0 --> K+K-pi0

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